Abstract
Chaotic systems can be used for secure communication and image encryption by applying a variety of encryption algorithms. While most of the low-dimensional chaotic systems and maps can be estimated by using phase reconstruction and thus the safety in signal processing and propagation is attacked. In this paper, an initial-dependent dynamical system, which is developed from the Rossler system by adding memristive function and disturbance function on the memristive variable z, is presented for realizing image encryption and bifurcation analysis is supplied in detail. Time-varying disturbance from sampled variables is applied to control the memristive variable and the dependence of mode oscillation on initial values is enhanced. As a result, the dynamics of this memristive system is switched between different oscillation modes (e.g., periodical to chaotic, chaotic to chaotic) by activating the initial value, memristive gain and disturbance gain, respectively. From a dynamical viewpoint, the involvement of stochastic adjustment on the memristive variable can reset the initial value and then induce time-varying parameter regulation or switch on certain parameter embedded in the memristive nonlinearity and function, and thus the dynamics dependence on the initial setting is enhanced. Standard bifurcation analysis is carried out on this memristive system and then the sampled time series are used for image encryption, furthermore, the reliability for this scheme is discussed and suggestions for further study are supplied in the end.